Band-pass filter network



April 22, 1 fJ-ffl H. A. WHEELER BAND-PASS FILTER NETWORK Filed May 25, 1958 Frequency Eni- FIGB.

lo L3 S Il FIGA.

INVENTOR yLD A.WHEELER BY f f I ATTORNEY Patented Apr. 22, 1941 BAND-'mss FILTER NETWORK Harold A. Wheeler, Great Neck, N. Y., assigner to Hazeltine Corporation, a corporation of Dela- Ware Application May23, 1938, Serial No. 209,442

iciaiiils. (ci. 173-44) i This invention relates to multiple-transformer selector systems for the transmission of a broad band of frequencies and, while the invention-is of general application, it is of particular utility as a phase-correcting network in band-pass signal-translating systems.

The ratio of cutoff frequencies of a transformer filter utilized in a band-pass selector system is limited by the coefficient of coupling of the transformer. It is diiiicult to construct a .transformer in which the coeiiicient of coupling between its windings is great and the inherent capacitance is small. To obtain a wider pass band, combinations of transformer filters having different pass bandshave been utilized.

In many electrical circuits it is desirable to translate signals of a wide range of frequencies through an electrical network with a predetermined phase shift Within the network or, in thecase of 4distortionless transmission, with a'phase shift in the network directly proportional to the frequency. For example, in the translation and amplification of video-modulated carrier-frequency signals in a television apparatus, it is required to translate signals overawide band including high frequencies. While it is desired' to translate such signals without distortion in each stage of the signal-translating channel, this may not be practicable, so that it is usually necessary to provide phase-correcting circuits in one or more stages of the signal-translating channel. Such phase-correctingcircuits may be utilized for the purpose of providing a. distortionless overall characteristic for the signal-translating channel or for the purpose of providing a given phase characteristic for one part of the signal-translating channel which is complementary to that of some other part of the channel.

Phase-correcting networks have heretofore been utilized for the purpose discussed above. In utilizing a phase-correcting sectionor network for a particular type of phase correction, it is usually necessary to select a type of section the phase shift of which varies in a generally desirable manner over the entire pass band of the system in which it is to be utilized and one which also has particularly favorable phase-correcting properties in selected portions of the pass band. In general, the frequency-phase shift characteristics of simpleband-pass filters have slope inthe middle of thepass bandzls particu-l larly useful in vcorrecting phase distortion; of such *a band-pass filter. Such aiilter section or network which tolerates substantial shunt capacitance across the terminal'circuits thereof is particularlyuseful in systems comprising circuit elements having appreciable inherent capacitance, such as vacuum tubes' having substantial interelectrode capacitance.

:It is an object of the invention, therefore, to provide a multiple-transformer band-pass filter network of' the type described above, requiring the minimum coefficients of'coupling consistent with the required cutoff frequencies.

It is a.' further objectof the invention to providea simplified multiple-transformer band-pass filter network of the type described above, pre-- senting. constant-k image impledances at the terminals thereof.

I t is another'object of the invention to provide a simplifiedmultiple-transformer band-pass filter Anetwork for passing a wide band of frequencies and having a nearly linear frequencyphase shift characteristic over the pass band.

It is a particular object of the invention to provide a 4two-transformer band-pass lter network, the slope of the frequency-phase shift characteristic of which is a maximum at the middle of the pass band.

It is anotherobject of the invention to provide'a network of the typendescribed above which will tolerate the maximum possible capacitance across the terminals thereof.

Itis a further object of the invention to provide a network of the type described above which will tolerate appreciable capacitance to ground from-each junction in the network.

In accordance with the invention, a band-pass filter comprises a plurality of transformers and c0ndensers,each of the transformers having primary and secondary winding-s and the number of condensersjfbeing two more than the Vnumber of transformer win-dings. The'transformer winding-s `and condensers are connected to form two ladder networks, one of the networks having the primary windings `as series arms ythereof and one-half of the .condensers as shunt arms there# of, and the other of 'the networks having the secondary windings as seriesl arms thereof 'and' theother half of the condensers'as shunt arms thereof. The reactive constants ,of the vladder networks-.are proportioned to secure a continuousv pass band between predetermined cutoff frequenclies. 'i f; f

In ua preferred "embodiment,l having maximum kslope of uthe frequency-phase shift characteristic in connection with the accompanying drawing, and its scope will be pointed out in the appended`` claims.

Referring now to the drawing, Fig. 1 isla cir-V cuit diagram of a lter network embodying the invention; Fig. 2 is a graph showing the frequency-phase shift characteristic of the circuit of Fig. 1; Fig. 3 illustrates an embodiment of the invention utilized t0 obtain constant-7c midseries image impedances across the terminals of the filter network; Fig. .4 illustrates an embodiment of the invention utilized to obtain midshunt constant-1c image impedances across the terminals of the network, while Fig. 5 is a graph showing the image impedance characteristics of the circuits of Figs. 1, 3, and 4.

Referring now more particularly to Fig. 1, there is shown a band-pass filter comprising two transformers, each having primary and secondary windings, and six condensers, the number of condensers being two more than the Anumber of transformer windings, which has maximum slope in its frequency-phase shift characteristic in the middle of the pass band. This lter comprises a first transformer having yprimary and secondary windings, L1, L1 and a second transformer having primary and secondary windings L2, L2 individually connected in series with the corresponding windings of transformers L1, L1 across a pair of input terminals l0 and a pair of output terminals l I, respectively. Resistors R, R individually connected to input terminals I0 and output terminals l I represent terminal resistors for the filter or the vimage impedances of adjacent `circuits to which the filter is coupled. Two condensers C3, C3 are provided, one connected in series Awith the primary coils L1, L2 and the-other connected in series with the secondary coils L1, L2. Additional shunt condensers C1, C1 and C2, C2 are provided for connection across the primary and secondary circuits and between the junctions of the primary and secondary windings and corresponding terminals of the primary and secondary circuits, respectively. The condensers in the circuit of Fig. 1 may be physical condensers or may be comprised in whole, or in part, of the inherent capacitance of other elements of the network or the system to which the network is coupled.

From the description given, it will be seen that the circuit of Fig. 1 comprises essentially two ladder networks, one having primary coils-L1, L2 as series arms and condensers C1, C2, C3 as shunt arms, and the other having vsecondary coils L1, L2 as series arms and condensersvC1, C2, C3 as shunt arms. By the term ladder network is meant any filter network having recurrent and alternating series and shunt impedance `arms such as that generalized type of structure shown in Fig. 1, page 121, of Transmission Circuits for Telephonie Communication by K. S. Johnson, 1927, published by D. Van Nostrand Company.

The frequency-phase shift characteristic of the circuitof Fig. 1 is illustrated in the graph of Fig. 2. It will, of course, beunderstoodlthat'the reactive constants of the ladder networks are proportioned to secure a continuous pass band between predetermined cutoff frequencies. It is seen that the slop-e of the frequency-phase shift characteristic of the embodiment of Fig. l, utilizing two transformers and having properly selected critical frequencies within the band, is a maximum at the center of the pass band. If more than two transformers are utilized, the effect is to cause the characteristic to be more nearly uniform over the pass band. l Transformer L1, L1 is more effective in the high-frequency portion ofthe pass band, while transformer L1, L2 ismore effective in the low-frequency portion of the band. Therefore, the slope of the frequency* phase shift characteristic in the upper part of the band can be decreased by increasing the coenicient of coupling of transformer L1, L1 and by decreasing the coeflicient of coupling of transformer L2.' L2, and vice versa. In designing a circuit to have a characteristic as shown in Fig. 2 for a particular application, the `following formulae may be used in connection with the circuit ofFig. 1:

Z1V=image impedance at either of terminals ID or .U 1c`=coeflicient of coupling vof each of transformers L1, L1 and L2, L2

and where-'fafa f3, f4," and f5 are, respectively, the frequencies in the pass band at which the phase shift of the filter of the invention is 1r, 211,31,

41T, and 51T. The subscripts of a particular angular frequency w identify it with the corresponding frequency.

n The formulae given above with reference to the circuit o f Fig. 1 are' derivedon the basis of equal coefficients of coupling between the two transformers. Equal 'coenicients of coupling yield Isubstantiallyv symmetrical phase and image kimpedance characteristics over the pass band when the band isr'elatively narrow or when the coefficient of coupling is muchless than unity. It -will'be understood that a relatively narrow band"is one in'which the band width is consider ably less than .themean 'frequency of the band. If thebandis not relatively narrow and if it is desired to secure symmetrical characteristics overthe band, transformer L1, L1 vshould have a coefficient of couplingsomewhat `less than that of transformer L2,'L2`. 'It will be understood that more Lthan vtwo 'transformers 'can be 'utilized in 1 the. filter of the invention, in which case additionaly condensers are utilized'.- and connected according to the system of' connection given above. The effect ofmorey than twov transformers is to provide a. very nearly uniforms'lope of the fre?- quency-phase shift characteristic `between thev cutoff frequencies of' the filter, except very close to the 'cutoff frequencies; v f

It will be understood that relations between critical frequencies other than thosef given in Equation 1 may be utilized. In prop'orti'oningacircuit in accordance with theinventi'on, the cir-- cuit. is. divided into its equivalent lattice net-- works in. accordance with the procedure described in detail in section 15 of' Theory of Electrical Artificial Lines and Filters,^ byv A. C. Bartlett (1931), published by John Wiley & Sons, Inc., New York. The critical frequencies. are then determined. from the equivalen-t lattice network;

Every critical frequency within the.- band.A is one L theory of electrical wave filters, by'H'. W. Bode, v

published in the Journal of Mathematics and Physics," November,l 1934. The constants of av circuit of theA inventionmay then be; determined from thexabove conditions.`

The circuit of Fig. 34 isv similar tof that of 1 and'l similar: circuit: elements have been given.. identical reference numerals. The circuit. of

Fig. 3 hasy addedy inductances La, I cf connected in series between pairs of terminals l0 and Il, respectively, and the ladder networks of the filter of the invention.

The circuit of Fig. 4 is entirely similar to the circuit of Fig. 3 except that series-connected inductances La have been replaced by inductances L4, L4 connected, as shunt arms of the ladder networks, in parallel with input terminals I0 and output terminals Il, respectively. Each of the ladder networks of the circuits of Figs. 3 and 4 is effective to present a constant-Ic form of image impedance to the pair of terminals to which it is coupled, the circuit of Fig. 3 being effective to present a constant-1c mid-series image impedance to each of its pairs of terminal circuits,

' while that of Fig. 4 is effective to present a constant-Ic mid-shunt image impedance to each of its Apairs of terminals. The image impedance characteristics for the filter networks of Figs. 3 and 4 are shown, respectively, by dotted-line curves I4 and l5 of Fig. 5, while the full-line curve i6 represents the image impedance which is presented to each pair of terminals by the ladder networks of Fig. 1.

In proportioning the circuits including the inductances La, L3 or L4, L4 of Figs. 3 and 4, respectively, the formulae given above are not applicable. The circuits are proportional in accordance with the general theory outlined above by resolving the networks into their equivalent lattice sections. The added series inductance L3 in the circuit of Fig. 3 has the maximum possible value consistent with the given image impedance and band width, namely,

LPX.:

while the shunt capacitance C1 in the circuit of' Fig. 4 likewise 'has the? maximumpossible val'uerl' i where Aw isnt-he` of. the` pass band in anguiar frequency. The phase. characterictics of and .scope of the. invention.

What is claimed is: v 1.- A band-pass filter comprising a plurality of transformers andlcondensers, each` of said transformersI having primary and secondary windings andthe number of said condensers being tWo morethan the number of said windings, said windings.v and condensers being connected to form two ladder networks, one of said networks having saidprirnary windings as series arms thereof and. one half of said. condensersY as shunt arms thereof and the other of said networks having said secondary windings as series arms thereof. andthe other half of said condensers as shunt arms thereof, the reactive constants of Said networks.. being proportioned to Secure a continuous pass band between predetermined cutoff frequencies.

2. A band-pass lter comprising two transformers and six condensers, each of ksaid transformers comprising primary and secondary windings, said windings and said condensers being connected in two ladder networks, one of said networks having said primary windings as series arms thereof and three of said condensers as shunt arms thereof, and the other of said networks having said secondary windings as series arms thereof and the remaining three of said condensers as shunt arms thereof, the reactive constants of said networks being proportioned to secure a continuous pass band between predetermined cutoff frequencies, whereby the slope of the frequency-phase shift .characteristic of said iilter has a maximum value in the middle of the pass band.

3. A band-pass filter comprising a plurality of transformers and a plurality of condensers, said transformers each having primary and secondary windings and the number of condensers being two more than the number of said windings, said windings and condensers being connected in two ladder networks, one of said networks comprising said primary windings as series arms thereof and one half of said condensers as shunt arms thereof, and the other of said networks comprising said secondary windings as series arms thereof and the other half of said condensers as shunt arms thereof, the reactive constants of said networks being proportioned to secure a continuous pass band and nearly uniform slope of the frequency-phase shift characteristic between predetermined cutoff frequencies.

4. A band-pass filter comprising a plurality of transformers and a plurality of condensers, each of said transformers having primary and secondary windings and the number of said condensers being two more than the number 01 said,

windings, said windings and condensers being connected in two ladder networks each comprising a pair of terminals, one of said networks having said primary windings as series arms and one half of said condensers as shunt arms, andthe other of said networks having said secondary windings asl series arms and the other half of said condensers as shunt arms, an additional inductance for each of said networks and coupled to the pair of terminals associated with the network, the reactive constants -of said networks being proportioned to secure a continuous pass band between predetermined cutoff frequencies and to present the constant-k form of image impedance at each-of said pairs of terminals. 1 1

5. A band-pass filter comprising a plurality of transformers and a plurality of condensers, each of said transformers having primary and secondary windings and the number of said condensers being two more than the number of said windings, said windings and condensers being connected in two ladder networks each comprising a pair of terminals, one of said networks having said primary windings as series arms and one half of said condensers as shunt arms, and the other of said networks having said secondary windings as series arms and the other half of said condensers as shunt arms, additional inductances individually connected in series with each pair of said terminals and the one of said networks associated therewith, the reactive constants of said networks being proportioned to secure a continuous pass band between predetermined cutoii frequencies, whereby the constant-k of transformers and a plurality of condensers, each of said ltransformers having primary and secondary windings and the number of said condensers being two more than the number of said windings, said. windings and condensers being connected in two ladder networks each comprising a pair of terminals, one oi' said networks having said primary windings as series arms and one half of saidconde'nsers as shunt arms, and the other of said networks having said secondary lwindings as series arms and the other half of said condensers as shunt arms, additional inductances individually connected across each of said pairs of terminals, the reactive constants of said networks being proportioned to secure a continuous pass bandbetween predetermined cutoff frequencies, whereby the constant-lc mid-shunt form of image impedance is presented by said networks at each of said pairs of terminals. 20

- 7. A band-pass filter comprising a plurality of transformers and a plurality of condensers, each of said transformers having primary and secconnected in two ladder networks, one of 'said networks having said primary windings as series arms and one half of said condensers as shunt arms, and the other of said networks having said secondary windings as series arms and the other half of said condensers as shunt arms, each of said ladder networks including an additional inductanoe connected as a shunt arm, the reactive constants of said networks being proportioned to secure a continuous pass band between predetermined cutoff frequencies and to present the constant-lc mid-shunt form of image impedance at each of said pair of terminals.

l HAROLD A. WHEELER. 

